In “Pluto Isn’t Sad, and You Shouldn’t Be Either”, there’s a line that’s easy to skip: Pluto was so faint and far away that for years nobody knew how big it was. Early guesses made it as big as the Earth. As measurements improved, it kept shrinking. How do you weigh something six billion kilometres away, that you can’t touch, that shows up in the best telescopes of the day as nothing more than a dot? You find something going round it.
The idea goes back to Johannes Kepler, who noticed in 1619 that the planets follow a strict pattern: the further a planet is from the Sun, the longer its year, and the cube of its distance divided by the square of its year comes out the same for every planet. Isaac Newton, about seventy years later, explained why, with his law of gravity, and in doing so added something Kepler hadn’t known. That constant ratio depends on the mass of the thing being orbited. A heavier Sun would pull harder, and planets at the same distances would have to whip round faster to avoid falling in.
Written out, Newton’s version says that the mass of the central body equals four times pi squared, times the orbit’s radius cubed, divided by the gravitational constant times the orbital period squared. You don’t need to know anything about the moon doing the orbiting, as long as it’s much smaller than its planet. You need only two numbers: how far away it goes round, and how long it takes. Measure those, and you can weigh the planet.
This is how we know the masses of almost everything in the solar system. The Moon’s distance and its month give the mass of the Earth. The Earth’s distance from the Sun and its year give the mass of the Sun. Galileo’s four moons of Jupiter, with their distances and periods, give the mass of Jupiter: about three hundred and eighteen Earths. Any world with a moon can be weighed this way.
For almost fifty years after it was discovered, Pluto had no known moon, and so it couldn’t be weighed directly. Astronomers had to estimate its mass from its brightness, guessing at its size and what it was made of, or from tiny tugs it might be giving to Neptune and Uranus, which turned out to be much too small to measure reliably. The estimates were all over the place, and many were far too big.
Then, in 1978, an astronomer named James Christy was examining photographs of Pluto taken at the US Naval Observatory. On some of them, Pluto’s image had a small bump on one side. On others, the bump was on a different side. He realised the bump was moving round Pluto, regularly, every six and a half days or so. It was a moon. It was named Charon, after the ferryman of the underworld in Greek myth.
Now Pluto could be weighed. Charon orbits about nineteen and a half thousand kilometres from Pluto, once every 6.387 days. Put those numbers into Newton’s formula and out comes a mass of about one and a half times ten to the twenty-two kilograms. That’s the combined mass of Pluto and Charon, since Charon is unusually large for a moon, about an eighth of Pluto’s mass; working out each one separately needed later, sharper observations. But the headline was immediate and startling. Pluto weighed only about a fifth of one per cent of the Earth. It was smaller than our own Moon. Decades of estimates collapsed overnight.
Charon turned out to be odd in another way. It is so big compared with Pluto that the two don’t so much have one going round the other as both going round a point in space between them, a point that lies above Pluto’s surface. They’re also locked face to face: Pluto always shows the same side to Charon, and Charon always shows the same side to Pluto, so from one hemisphere of Pluto, Charon hangs forever in the same spot in the sky.
And the method that weighed Pluto also helped demote it. When Eris was discovered in 2005, it too had a moon, later named Dysnomia. Measure Dysnomia’s orbit, apply the same formula, and Eris comes out about a quarter more massive than Pluto. That single calculation, with nothing but a distance, a time and a constant of nature, was part of what forced astronomers in 2006 to decide, at last, what a planet is.